We have a function h(x).
We have to come up with two functions that, when compounded, they give as result h(x).
This compounding of two functions can be expressed as:
[tex](f\circ g)(x)=f(g(x))=h(x)[/tex]
This means that when the function g(x) is the argument of f(x), the result is h(x).
The definition of h(x) is:
[tex]h(x)=\sqrt{7x^2+9x-74}[/tex]
We then can think of a compound function like this: one function is the quadratic equation and the other function is he square root.
Then, we can try with:
[tex]\begin{gathered} f(x)=\sqrt{x} \\ g(x)=7x^2+9x-74 \end{gathered}[/tex]
Then, if we now apply the compounding we obtain:
[tex]\begin{gathered} (f\circ g)(x)=f(g(x)) \\ (f\circ g)(x)=\sqrt{g(x)} \\ (f\circ g)(x)=\sqrt{7x^2+9x-74} \\ (f\circ g)(x)=h(x) \end{gathered}[/tex]
So the functions proposed are correct.
Answer: f(x) = √x and g(x) = 7x²+9x-74.
